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Parametric surfaces are particularly handy if you are unable to find
any data to play with right away. Parametric surfaces are surfaces
parametrized typically by 2 variables, u and v. VTK has a bunch of
classes that let users explore Parametric surfaces. This
functionality is also available in Mayavi. The data is a 2D
surface embedded in 3D. Scalar data is also available on the surface.
More details on parametric surfaces in VTK may be obtained from Andrew
Maclean’s Parametric Surfaces document.

After starting mayavi2, create a simple Parametric surface source
by selecting File->Load data->Create Parametric Surface source.
Once you create the data, you will see a new node on the Mayavi
tree view on the left that says ParametricSurface. Note that
you will not see anything visualized on the TVTK scene yet.

You can modify the nature of the parametric surface by clicking
on the node for the ParametricSurface source object.

To see an outline (a box) of the data, navigate to the
Visualize->Modules menu item and select the Outline module.
You can also right-click on the ParametricSurface node to bring up
a context menu and select Add Module->Surface.
You will immediately see a wireframe cube on the TVTK scene.
You should also see two new nodes on the tree view, one called
Colors and legends and one underneath that called Outline.

You can change properties of the outline displayed by clicking on
the Outline node on the left. This will create an object editor
window on left bottom of the window (the object editor tab) below
the tree view. Play with the settings here and look at the
results. For example, to change the color of the outline box
modify the value in the color field. If you double-click a node on
the left it will pop up an editor dialog rather than show it in the
embedded object editor.

To view the actual surface create a Surface module by selecting
Visualize->Modules->Surface. You can show contours of the
scalar data on this surface by clicking on the Surface node on
the left and switching on the Enable contours check-box.

To view the color legend (used to map scalar values to colors),
click on the Modules node on the tree view. Then, on the ‘Scalar LUT’
tab, activate the Show scalar bar check-box. This will show
you a legend on the TVTK scene. The legend can be moved around on
the scene by clicking on it and dragging it. It can also be
resized by clicking and dragging on its edges. You can change the
nature of the color-mapping by choosing among different lookup
tables on the object editor.

You can add as many modules as you like. Not all modules make
sense for all data. Mayavi does not yet grey out (or disable) menu
items and options if they are invalid for the particular data
chosen. This will be implemented in the future. However making a
mistake should not in general be disastrous, so go ahead and
experiment.

You may add as many data sources as you like. It is possible to
view two different parametric surfaces on the same scene by selecting
the scene node and then loading another parametric surface source.
Whether this makes sense or not is up to the user. You may also
create as many scenes you want to and view anything in those.
You can cut/paste/copy sources and modules between any nodes on
the tree view using the right click options.

To delete the Outline module say, right click on the Outline
node and select the Delete option. You may also want to
experiment with the other options.

You can save the rendered visualization to a variety of file
formats using the File->Save Scene As menu.

The visualization may itself be saved out to a file via the
File->Save Visualization menu and reloaded using the Load
visualization menu.

Shown below is example visualization made using the parametric
source. Note that the positioning of the different surfaces were effected by moving the actors on screen using the actor mode of the
scene via the ‘a’ key. For more details on this see the section on
Interaction with the scene.